This invention relates to a compression ignition, direct injection internal combustion engine, and particularly to such an engine, having at least one cylinder with an associated piston which has a combustion chamber or cavity in the form of a body of rotation disposed in its head to receive almost the entire quantity of combustion air at the end of the compression stroke, this chamber including a constriction of the piston which divides the chamber into an upper and a lower part. The engine will also have an injection nozzle which is mounted in the cylinder such that the nozzle tip will be at least near the axis of the chamber, its fuel jets will be directed towards the wall of the combustion chamber in the piston, and the geometrical points of intersection of the axes of its nozzle holes will lie below the narrowest cross-section of the constriction in the combustion chamber in the piston throughout the entire injection period.